840edo

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840edo

841edo →

Prime factorization	23 × 3 × 5 × 7
Step size	1.42857 ¢
Fifth	491\840 (701.429 ¢)
Semitones (A1:m2)	77:65 (110 ¢ : 92.86 ¢)
Dual sharp fifth	492\840 (702.857 ¢) (→ 41\70)
Dual flat fifth	491\840 (701.429 ¢)
Dual major 2nd	143\840 (204.286 ¢)
Consistency limit	7
Distinct consistency limit	7
Special properties	Highly composite

840 equal divisions of the octave (abbreviated 840edo or 840ed2), also called 840-tone equal temperament (840tet) or 840 equal temperament (840et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 840 equal parts of about 1.43 ¢ each. Each step represents a frequency ratio of 2^1/840, or the 840th root of 2.

840edo is the 15th highly composite edo, and it is the first one divisible by 7. It does not tune the 9-odd-limit consistently, though a reasonable 13-limit interpretation exists through the patent val. A comma basis for the 13-limit is 729/728, 1575/1573, 67392/67375, 804375/802816, 250047/250000.

Odd harmonics

Approximation of odd harmonics in 840edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.526	-0.599	-0.254	+0.376	+0.111	-0.528	+0.303	-0.670	-0.370	+0.648	+0.297
	Relative (%)	-36.9	-42.0	-17.8	+26.3	+7.7	-36.9	+21.2	-46.9	-25.9	+45.3	+20.8
Steps (reduced)		1331 (491)	1950 (270)	2358 (678)	2663 (143)	2906 (386)	3108 (588)	3282 (762)	3433 (73)	3568 (208)	3690 (330)	3800 (440)